Algebra Guide

Quadratic Formula Examples: Roots and Discriminant

Understand the formula, the discriminant, and signs that often cause wrong answers. This guide keeps the math practical, so you can understand what to enter, why it works, and how to spot an answer that does not make sense.

Quick Answer

Use the quadratic formula when an equation is in the form ax^2 + bx + c = 0 and factoring is not obvious.

Plain-language ruleIdentify a, b, and c.

When to Use This

This topic is useful when a problem looks familiar, but you are not sure which button, formula, or order of steps to use. Start by naming the goal in normal words, then translate it into the calculator setup.

equations with one unknown
checking whether a solved value works
turning a word problem into symbols

Step-by-Step Method

Identify a, b, and c.
Calculate b^2 - 4ac.
Put the values into the formula.
Simplify both plus and minus answers.

After you get the answer, do one quick reasonableness check. Ask whether the answer should be bigger or smaller than the starting number, whether the unit is correct, and whether a rounded answer is acceptable.

Calculator Tips

Write one line per operation so signs stay visible.
Do the same thing to both sides of the equation.
Always substitute your answer back into the first equation.

Worked Example

Solve x^2 - 5x + 6 = 0

Here a = 1, b = -5, and c = 6. The formula gives roots 2 and 3.

Common Mistakes

Changing one side of an equation but not the other.

Pause and check this before trusting the final answer. A small setup mistake can make the calculator look wrong even when it only followed the input.

Losing a negative sign while moving terms.

Pause and check this before trusting the final answer. A small setup mistake can make the calculator look wrong even when it only followed the input.

FAQ

Can I use a calculator for this?

Yes. A calculator helps with arithmetic, but the important part is choosing the right formula and entering the values in the right places.

How should I check my answer?

Estimate first, then substitute the answer back into the problem or reverse the operation. If the result is wildly larger or smaller than expected, recheck the setup.